In mathematics

the smallest proper prime, a prime p which ends in the digit 1 in base 10 and whose reciprocal in base 10 has a repeating sequence with length p − 1. In such primes, each digit 0, 1, ..., 9 appears in the repeating sequence the same number of times as does each other digit (namely, p − 1/10 times).[2]:166

a Pillai prime since 8! + 1 is divisible by 61 but 61 is not one more than a multiple of 8.[7]

a Keith number, because it recurs in a Fibonacci-like sequence started from its base 10 digits: 6, 1, 7, 8, 15, 23, 38, 61...[8]

palindromic in bases 6 (1416) and 60 (1160)

In the list of Fortunate numbers, 61 occurs thrice, since adding 61 to either the tenth, twelfth or seventeenth primorial gives a prime number[9] (namely 6,469,693,291; 7,420,738,134,871; and 1,922,760,350,154,212,639,131).

U.S. Route 61 is the highway that inspired so much attention on "Highway 61"

Part 61 is a law created by the FAA regarding medical exams. This law has often come under attack by AOPA.

The P-61 is the Northrop designed fighter first designated as the XP-61. It first flew on May 26, 1942. It is also known as the Black Widow as it was the first fighter aircraft designed to be a night fighter